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Inegalitate in n variabile

Posted: Sun May 10, 2009 7:49 pm
by alex2008
Fie \( x_1,x_2,...,x_n> 0 \) astfel incat \( \sum_{k=1}^n\frac{1}{1+x_k}=1 \) . Sa se demonstreze ca :

\( x_1x_2...x_n\ge n^{n+1} \)

Posted: Sun May 10, 2009 9:16 pm
by Marius Mainea
\( x_k=\frac{\sum_{i\neq k}a_i}{a_k} \) si apoi AM-GM.